Calculus of Variations and Geometric Measure Theory

E. Mukoseeva

Second variation techniques for stability in geometric inequalities

created by mukoseeva on 14 Apr 2021


Ph.D. Thesis

Inserted: 14 apr 2021
Last Updated: 14 apr 2021

Year: 2020

The corrected version of my thesis


We study stability of minimizers for several geometric problems. Applying second variation techniques and some free boundary regularity results we are able to prove sharp quantitative isocapacitary inequality, both in the case of standard capacity and that of $p$-capacity. With the same approach we deduce that charged liquid droplets minimizing Debye-Hückel-type free energy are spherical in the small charge regime.